# Properties

 Label 59248e Number of curves $2$ Conductor $59248$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 59248e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59248.y2 59248e1 $$[0, -1, 0, -84, 224]$$ $$21296/7$$ $$21803264$$ $$[2]$$ $$10752$$ $$0.11112$$ $$\Gamma_0(N)$$-optimal
59248.y1 59248e2 $$[0, -1, 0, -544, -4560]$$ $$1431644/49$$ $$610491392$$ $$[2]$$ $$21504$$ $$0.45770$$

## Rank

sage: E.rank()

The elliptic curves in class 59248e have rank $$0$$.

## Complex multiplication

The elliptic curves in class 59248e do not have complex multiplication.

## Modular form 59248.2.a.e

sage: E.q_eigenform(10)

$$q + 2 q^{3} - 2 q^{5} - q^{7} + q^{9} - 2 q^{13} - 4 q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.